Linear Operators: Spectral theory |
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Page 1000
... uniformly on each compact subset on the half - plane ( 2 ) > 0. If { ƒn } were known to be uniformly convergent in a neighborhood of U , the analyticity of its limit fy would be clear . Unfortunately it is not clear that the sequence f ...
... uniformly on each compact subset on the half - plane ( 2 ) > 0. If { ƒn } were known to be uniformly convergent in a neighborhood of U , the analyticity of its limit fy would be clear . Unfortunately it is not clear that the sequence f ...
Page 1001
... uniformly on any portion of Q whose closure contains neither a nor b . Let M be a bound for the sequence yn so that ... uniformly on Q to the function g given by the equations g ( z ) = f ( z ) ( z - a ) 2 ( z — b ) 2 , - za , b , z = a ...
... uniformly on any portion of Q whose closure contains neither a nor b . Let M be a bound for the sequence yn so that ... uniformly on Q to the function g given by the equations g ( z ) = f ( z ) ( z - a ) 2 ( z — b ) 2 , - za , b , z = a ...
Page 1108
... uniformly in i , ∞ ( ii ) lim , Σ , 2 , ( m ) * = 0 uniformly in m , it follows that i = r ( iii ) 1λ ( m ) * is bounded uniformly in m , ( iv ) λ ( m ) → 0 as i → ∞ uniformly in m . Thus , by the above inequality , lim II ( 1 + 2 ...
... uniformly in i , ∞ ( ii ) lim , Σ , 2 , ( m ) * = 0 uniformly in m , it follows that i = r ( iii ) 1λ ( m ) * is bounded uniformly in m , ( iv ) λ ( m ) → 0 as i → ∞ uniformly in m . Thus , by the above inequality , lim II ( 1 + 2 ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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A₁ adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers continuous function converges Corollary countably deficiency indices Definition denote dense eigenfunctions eigenvalues element equation essential spectrum Exercise exists f₁ finite dimensional follows from Lemma follows from Theorem formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator homomorphism identity inequality infinity integral interval kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence shows solution spectral set spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology tr(T transform uniformly unique unitary vanishes vector zero